1. Are you asking about webmail storage on the server?
I don't think AT&T limits it. If you want to be sure, ask AT&T support.
2. How did you access your RoadRunner emails? If your RoadRunner
emails are already downloaded to your hard drive, they will stay there.
Not sure what you mean by "Move to new". Are you also changing
your email client program?
Mail providers are independent of one's email client program.
3. Check out the posts from U-verse users here:
Gary VanderMolen, Microsoft MVP (Mail)